Archive Page template by category but excluding some. WP 2.5

Hey Gang,
I’m hoping to get some coding help here. I’m not bad at manipulating PHP, but I’m crap at writing it, so I’m hoping someone with a little extra time and a generous spirit can help me out.

I’ve got an Archive template which calls each category in alphabetical order followed by it’s associated posts. My code looks like this:

<?php $cats = get_categories("hierarchical=0"); ?>

<?php if($cats != NULL) { ?>
		<ul>
		<?php foreach ($cats as $cat) { ?>
			<li>

			<?php if($cat != NULL) {
				$base_url = get_bloginfo('home') . "/category/" . $cat->slug; ?>
				<h3><a href="<?php echo $base_url?>"><?php echo $cat->cat_name?></a></h3>
			<?php } ?>

			<?php // Show category description
				if ($cat->category_description != NULL) ?>
					<p><?php echo $cat->category_description ?></p>

				<?php $myposts = get_posts("category=$cat->cat_ID"); ?>
				<ul>
				<?php foreach($myposts as $post) : ?>
					<li><?php the_time('M d') ?>. <a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></li>
				<?php endforeach; ?>
				</ul>
			</li>
	<?php } ?>
		</ul>
<?php } ?>

But now I’ve created categories which I want to exclude from this list but have absolutely no idea where to begin.

Thanks a million (in advance) for any help you can provide. Like I said, I’m no good at writing php syntax, so if you could give a code example that would be infinitely helpful.

Thanks!